If you are talking about the vampire attacks, they shouldn't, as they only happen when you are in the area. You'll probably find that while you are in solstheim, nothing at all will happen in Skyrim.
Nothing happens if you aren't in the area.
E.g you will never arive in a city to find a dragon has already attacked and half the citizens are dead.
I should point out that I have only done the Dawnguard side of the questline, so if the blacksmith's deaths are something to do with the vampire side of it, I wouldn't know. But I still doubt it as I'm not aware of any time-sensitive quests.